Spaces of type H∞+C

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A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that H∞+C is a closed subalgebra of L∞. In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.

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@article{Rudin1975, abstract = {A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that $H^\infty +C$ is a closed subalgebra of $L^\infty $. In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.}, author = {Rudin, Walter}, journal = {Annales de l'institut Fourier}, language = {eng}, number = {1}, pages = {99-125}, publisher = {Association des Annales de l'Institut Fourier}, title = {Spaces of type $H^\infty +C$}, url = {http://eudml.org/doc/74216}, volume = {25}, year = {1975},}

TY - JOURAU - Rudin, WalterTI - Spaces of type $H^\infty +C$JO - Annales de l'institut FourierPY - 1975PB - Association des Annales de l'Institut FourierVL - 25IS - 1SP - 99EP - 125AB - A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that $H^\infty +C$ is a closed subalgebra of $L^\infty $. In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.LA - engUR - http://eudml.org/doc/74216ER -